Currently proposed very high speed transmission systems over optical fiber at 100 Gbps and beyond use multiple bits per symbol as well as multiple polarizations in order to reduce the cost and complexity of the design. For example, a typical implementation may include two polarizations used with Quadrature Amplitude Modulation (QAM) (such as Quadrature Phase Shift Keying (QPSK)) on two orthogonal carriers on each polarization. At the receiver of such a system, the two polarizations are typically recovered in an optical module where the quadrature signals are demodulated to baseband and converted to the two quadrature electrical signals for each polarization. One of the key functions of such a receiver is to determine a timing point of the data such that the sampling point falls in the center of the recovered analog waveform. Methods of timing recovery have been proposed in Y. Wang et al., “An alternate Blind Feedforward Symbol Timing Estimator Using Two samples par Symbol”, IEEE Transactions on communications, Vol. 51, No. 9, September, 2002, pp 1451-1455; F Gini et al., “Frequency Offset and Symbol Timing Recovery in Flat-Fading Channels: a Cyclostationary Approach”, IEEE Transactions on communications, Vol. 46, No. 3, March, 1998, pp 400-411; and Y. Wang et al., “Blind Feedforward Symbol Timing Estimator for Linear Modulations”, IEEE Trans on Communications, Vol 3, No 3, May 2004, pp 709-715. These methods typically use a non linearity to generate a spectral component at two or higher over sampling rates and apply to a single possibly complex input signal.
High speed transmission over optical fiber suffers from a number of well known impairments. In particular the signal is subjected to Polarization-mode dispersion (PMD) where the signal on one polarization at the receiver is a mixture of the two polarization signals transmitted, chromatic dispersion (CD) where the signal is subjected to a parabolic increasing phase distortion along the fiber, polarization dependent loss (PMD) where the gain of the two polarizations is not the same, and polarization delay imbalance where the travel time of the two polarizations is not the same. The methods described above may be used to detect the timing on a single two times oversampled QAM signal. However, after mixing of the two polarizations, the timing estimate disappears for certain combinations of polarization delay and angle. Thus in the presence of arbitrary PMD and PDL impairments, no reliable timing estimate can be derived.
Chromatic dispersion (CD) and polarization mode distortion (PMD) are key linear distortions that limit the performance of optical communication systems. Traditional direct-detect systems operating at 10 Gbps or lower rates employ dispersion compensating fiber to mitigate CD. Due to recent advances in GHz digital signal processing capability, systems operating at 40 Gbps and 100 Gbps use coherent transceivers employing electronic dispersion compensation (EDC) technology to mitigate both CD and PMD. Regardless of the specific architecture partitioning and its time vs. frequency implementation choice, EDC digital filters require correct sample phase timing to be established by the receiver. Timing recovery corrects for the phase and frequency offset between the transmitter and receiver clocks, and is often performed digitally by filtering the spectral line that appears at the symbol rate after squaring the received signal. These algorithms typically require four samples per symbol such as in M. Oerder & H. Meyr, “Digital Filter and Square Timing Recovery”, IEEE Transactions on Communications, Vol. 36, No. 3, March 1988, although variants requiring only two samples per symbol also exist such as in Y. Wang et. al., “An Alternative Blind Feedforward Symbol Timing Estimator Using Two Samples Per Baud”, IEEE Transactions on Communications, Vol. 51, No. 9, September 2003; and Y. Yang et. al., “Performance Analysis of a Class of Nondata-Aided Frequency Offset and Symbol Timing Estimators for Flat-Fading Channels”, IEEE Transactions on Signal Processing, Vol. 50, No. 9, September 2002.
The CD parameter, χ, is defined as χ≡DL wherein D is the dispersion parameter of a fiber and L is the fiber length. A key problem of practical importance is the computation of the CD parameter χ since this single parameter determines the tap weights of the required equalizer, for either a time-domain or a frequency-domain implementation. The value of χ may be totally unknown on short haul links, or perhaps known only to a finite tolerance of ±1500 ps/nm on typical long haul links. In either case, χ must be estimated with suitable accuracy in the presence of all channel impairments in order to solve for the CD equalization parameters. Transmission of a known periodic training signal provides one solution since the received signal may be used to compute the inverse transfer function of the CD if the transmitted signal is known. The training sequence must be retransmitted at a rate faster than the expected temporal variation of the CD response with temperature. This method is unattractive as it fails in the presence of significant PMD, and since a portion of the channel bandwidth must be devoted to the training sequence overhead. The training sequence duration may span several hundreds of taps for 100 Gbps systems with CD approaching 40,000 ps/nm.
Other approaches involve transmitting known in-band subcarriers or pilot tones and monitoring the RF tones at the receiver such as in T. Dimmick et al., “Optical Dispersion Monitoring Techniques Using Double Sideband Carriers”, IEEE Photonics Technology Letters, Vol. 12, No. 7, July 2000. These approaches use non-standard transmitters, transmitter modifications, or have high cost and complexity. Still another approach to CD monitoring involves extracting clock frequency components from the received signal. The differential phase between clock components provides one mechanism for CD monitoring such as in B. Fu et al., “Fiber Chromatic Dispersion and Polarization-Mode Dispersion Monitoring Using Coherent Detection”, IEEE Photonics Technology Letters, Vol. 17, No. 7, July 2005. The overall power of the extracted clock component provides another mechanism such as in S-M. Kim et al., “The Efficient Clock-Extraction Methods of NRZ Signal for Chromatic Dispersion Monitoring”, IEEE Photonics Technology Letters, Vol. 17, No. 5, May 2005. These methods employ radio frequency (RF) processing with tight analog band pass filtering to extract the clock signals, requiring additional components and complexity at the receiver.
So-called “blind” solutions not requiring the transmission of a training sequence are also popular in practice. In these cases, a traditional metric of the received signal such as (i) detecting phase modulation to intensity modulation due to CD such as in M. Tomizawa et al., “Nonlinear Influence on PM-AM Conversion Measurement of Group Velocity Dispersion in Optical Fibers”, Electronics Letters, Vol. 30, No. 17, August 1994; (ii) recovered Q-factor such as in I. Shake et al., “Quality Monitoring of Optical Signals Influenced by Chromatic Dispersion in a Transmission Fiber Using Averaged Q-factor Evaluation”, IEEE Photonics Technology Letters, Vol. 13, No. 4, April 2001; or (iii) signal-to-noise ratio (SNR) is evaluated and used to evaluate the quality of a given estimate {circumflex over (χ)} of χ, or equivalently the current CD equalizer settings. The key drawback of these approaches is that typical metrics such as Q-factor or SNR provide no direct relationship to the desired setting χ or the error ({circumflex over (χ)}−χ) in the current setting {circumflex over (χ)}, or even if the current setting should be increased or decreased in order to improve performance. Consequently, such solutions lead to complex and inefficient “exhaustive searches” where the signal metric must be evaluated for all possible candidate settings for {circumflex over (χ)} ((ie. the full range of χ).
A typical example of this “blind search” approach is described in M. Kuschnerov et al., “DSP for Coherent Single-Carrier Receivers”, IEEE Journal of Lightwave Technology, Vol. 27, No. 16, August 2009. The algorithm evaluates for every possible value of CD setting χ a metric based on Godard's original CMA equalizer that measures the deviation from constant amplitude of the CD equalizer output. The minimum obtained metric identifies the best setting for the CD equalizer. A “two-pass” search is proposed where the first pass uses coarsely spaced settings for χ, and then a second pass uses a set of finely spaced settings centered around the best setting found by the first pass. One large drawback of this algorithm is its complexity. Evaluation of the Godard metric is costly in computation and is required solely for identifying the proper χ setting; these computations are not shared nor required by any other transceiver functions. This complexity burden is amplified by the inefficiency of the two-pass blind search. Finally, the accuracy of the algorithm given by Kuschnerov et al. degrades significantly as the amount of PMD increases. Ideally, any metric-based solution should provide the same accuracy for χ independent of level of PMD/PDL distortion.
One alternative solution to the metric-based “blind searches” for the CD setting χ involves combining the CD and PMD/PDL digital filters into a single “butterfly” structure that addresses both CD and PMD/PDL distortions. Then an adaptive algorithm such as CMA or LMS provides a solution for the time-varying tap weights of the complete structure. This approach no longer requires an explicit solution for the CD setting χ, but instead incurs a significant complexity burden. The “butterfly” structure requires the adaptation of hundreds of taps to handle both CD and PMD/PDL, whereas adaptation of only tens of taps is required to handle PMD/PDL for typical 100 Gbps systems desired to span 2000 km links.